An apparatus of this type is disclosed in EP-A2-0 801 382. This apparatus is suitable for the use of optical recording media having data markings both in the track and in the intermediate track, so-called land and groove recording media. The known apparatus may be regarded as having the disadvantage that it is not possible, during the traversal of the tracks in the radial direction during the use of such recording media, to obtain information about the direction in which the light beam traverses the tracks of the recording medium. The so-called mirror signal which is generated for this purpose in the case of conventional data media and detects a region free of data markings, the so-called mirror area, has a doubled frequency in the case of land and groove recording media. Owing to the data markings that are present there, the track and (intermediate track) have a lower reflectivity than the region located between track and intermediate track, in which region the mirror signal is then at a maximum. Consequently, a comparison of the phase angle of the track error signal and of the mirror signal for the purpose of direction identification is no longer meaningful, on account of the doubled frequency of the mirror signal.